An instance is an in-game area where players can encounter enemies or other players. Instances help balance the server load of players and also make it easier for players to move about and see objects such as vendors.
Most instances, such as the Waterworks, many wilderness adventure areas and raids are private. That is, on entering the quest, only the player and members of his party will see the quest area and its contents. They will not see other parties who are playing the same quest, as each party will have their own instance.
Some instances can be public. The Marketplace is a common public non-combat instance where players can pick up quests, meet vendors and visit their Guild. The map compass has a drop-down menu where players can switch to a numbered instance should other members of their party or guild materialize in a different public instance.
A Guild's airship is the most private instance, where only members of that guild can enter, save for invited guests.
Public instances are sometimes used for combat. Examples include the Mabar Endless Night Festival and the Treasure of Crystal Cove. Again, the map compass allows players to group together when they find themselves in separate instances.